The songwriting ability and vocal harmonies of the bassist Dan Peek, who has died aged 60, were an integral part of the success of the soft-rock band America. Between 1971 and 1977, the year he quit for a solo career, Peek and his bandmates, Dewey Bunnell and Gerry Beckley, scored an impressive run of hit singles and albums, mostly in their native US. The biggest of these was their debut single, A Horse With No Name, which made the top three on both sides of the Atlantic and instantly earmarked them as the new Crosby, Stills & Nash.

Like his fellow band members, Peek was the son of a US military serviceman and his early years were peripatetic. Born in Florida, he had already lived in Greenland, South Carolina and Japan before the age of 10. The frequent travel meant long journeys on the US highway, where Peek first began singing three-part harmonies with his brother Tom and sister Debbie. By the time his father transferred to an army base in West Ruislip, Middlesex, in 1967, Peek had also become a proficient guitarist and piano player.

It was while attending London Central high school (for the children of US service personnel) in Bushey that he met Bunnell and Beckley. "We really hit it off as friends long before we became bandmates," Peek told me when I interviewed him two years ago. "We immediately bonded as we were all obsessed with music. "Eventually I joined Gerry and two of his mates in a band called the Daze." In 1969 Peek left for a brief spell at university in the US, and Bunnell took his place in the fledgling group.

On his return they became a trio, fired by the acoustic Americanisms of Crosby, Stills, Nash & Young, James Taylor and Joni Mitchell. They were still broke though, and for a time were forced to rehearse in Bunnell's car. "From the summer of 1970 until our first album was released in 1972, we rehearsed four hours or more per day," explained Peek. "Dewey's Morris Minor was actually a great space to practice, as it had an immediacy and closeness that helped in really hearing the intricate harmonies and guitar licks we were fine-tuning."

The band secured early gigs at hippy hangouts in London such as Middle Earth and the Roundhouse, before landing a contract with Warner Brothers. While scouting for a record deal, Peek and Bunnell were still employed as dishwashers at the base cafeteria. "There was an 'Americana' brand jukebox there that we played constantly," said Peek. "Somehow the connection between its music and our quest for a name dovetailed. I pushed for keeping it simple and direct, hence America."

A Horse With No Name, issued in December 1971, was an immediate success. Their smooth harmonies and readily accessible folk-rock sound chimed with the times, as did the hirsute wholesomeness of their image. Their first album, America, was a colossal hit too, reaching No 1 in their homeland, chalking up more than a million sales and earning them a Grammy for best new artist. Their follow-up, Homecoming (1972), which featured Peek's first great composition, Don't Cross the River, was only marginally less popular.

For their fourth album, Holiday (1974), the band drafted in George Martin as producer, who helped frame their songs in clever arrangements and give them a glossy studio punch. Lonely People released in December, became Peek's signature tune and made the US top five. A year later America scored their second US No 1 with Beckley's Sister Golden Hair.

But all was not as ripple-free as the music suggested. Tensions had long been part of the band's dynamic. "All three of us were enormously competitive and it was a high-stakes game we were playing," admitted Peek. "And what had once been an all-for-one camaraderie evaporated. It could get pretty ugly." Peek's increasing drug dependency was also becoming a problem. "I was taking hash, marijuana, cocaine, quaaludes, alcohol and tobacco. …There was a certain amount of naivety regarding drug use in the 60s and 70s. In retrospect I sincerely wish I'd been a teetotaller." He left the group by mutual consent in the summer of 1977.

Peek duly set about overhauling his life. He vowed to kick his addictions and renewed his faith in Christianity. His debut solo single, All Things Are Possible, issued on Pat Boone's Lamb & Lion label in 1979, became one of Christian rock's first big crossover hits, while Bunnell and Beckley contributed to the album of the same name. But despite the occasional on-stage reunion over the next couple of decades, America remained a duo.

By the 1990s Peek had more or less retired from the music circus, preferring instead to record at home in the Cayman Islands. Later years yielded an autobiography, An American Band (2004), and a steady trickle of albums, mostly released via his website. The most recent was All American Boy in 2007.

He is survived by his wife, Catherine.

• Dan Peek, guitarist, singer and songwriter, born 1 November 1950; died 24 July 2011